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Long-time evolution and regions of existence of parametrically excited nonlinear cross-waves in a tank

Published online by Cambridge University Press:  26 April 2006

Lev Shemer  and
Eliezer Kit
Lev Shemer
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat-Aviv 69978, Israel
Eliezer Kit
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat-Aviv 69978, Israel
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Abstract

Results of an experimental and numerical study of parametrically excited nonlinear cross-waves in the vicinity of the cut-off frequency, are reported. Experiments are performed at three cross-wave modes and in the whole range of existence of cross-waves. Numerical studies are based on the solution of the nonlinear Schrödinger equation with a boundary condition at the wavemaker which corresponds to parametric excitation. The validity of the scaling procedure adopted in the model is verified experimentally. Dissipation is incorporated in the model equation and in the wavemaker boundary condition. The influence of the wave breaking on the range of existence of cross-waves is discussed and the relation between the maximum possible steepness of cross-waves and the limits of their existence is obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 249 - 263
Copyright
© 1989 Cambridge University Press

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